Problem: A sphere is cut into four congruent wedges. The circumference of the sphere is $12\pi$ inches. What is the number of cubic inches in the volume of one wedge? Express your answer in terms of $\pi$.

Note: To measure the circumference, take the largest circle on the surface of the sphere.
Answer: Let the sphere's radius be $r$.  From the sphere's circumference we have $2\pi r = 12\pi$; solving for $r$ yields $r = 6$.  The volume of the sphere is $\frac{4}{3}\pi r^3 = \frac{4}{3}\pi (6^3) = 36\cdot 8 \pi$.  The volume of one wedge is one-fourth this volume, or $\frac{1}{4} \cdot 6^2\cdot 8 \pi = 6^2\cdot 2\pi = \boxed{72\pi}$.